Something you can try:
If you have a primer bulb, prime with 4 - 5 pushes and start. When you hear it getting ready to stall, push the primer bulb as many times as required to allow the motor to recover and run. You may have to do this several times until it warms up.
I have a 5hp, horizontal shaft Tecumseh on one piece of equipment and this is how I must start it when it's cold. After it warms up, it starts normally. It has been that way since day 1. I'm not sure if it's a Tecumseh trait or not but it will cost nothing to try.
Rich